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If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which

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If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which 10^p is a factor of m?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


OA C

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Re: If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which

by ManhattanElitePrep » Mon Dec 20, 2021 8:57 am
If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which 10^p is a factor of m?(A) 7(B) 8(C) 9(D) 10(E) 11

Given: m=40! So we should find the # of trailing zeros in 40!, as it'll be the greatest value of p for which 40!/10^p will be an integer.

40! has 9 trailing zeros, which means that 40! ends with 9 zeros so p=9 is the greatest integer for which 10^p (10^9) is a factor of 40!.

Answer: C.

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Re: If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which

by regor60 » Mon Dec 20, 2021 12:59 pm
5 is the largest prime that's a factor of 10, so should be the limiting part

5-20 has 4 fives
25 has 2
30-40 has 3

9 total
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